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Math Help - Limits

  1. #1
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    Limits

    What does the function f(x)=1-2^(-x) approach as x goes to infinity?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by lilikoipssn View Post
    What does the function f(x)=1-2^(-x) approach as x goes to infinity?
    \lim_{x\to\infty}[1-2^{-x}]

    Using our laws of limits and algebra we rewrite this as

    \lim_{x\to\infty}1-\lim_{x\to\infty}\frac{1}{2^{x}}

    and we get 1-\frac{1}{2^{\infty}}=1-0=1
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  3. #3
    Moo
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    Quote Originally Posted by Mathstud28 View Post

    and we get 1-\frac{1}{2^{\infty}}=1-0=1
    You'd better write 1-\lim_{x \to \infty} \frac{1}{2^x}

    .
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Moo View Post
    You'd better write 1-\lim_{x \to \infty} \frac{1}{2^x}

    .
    I was trying to be practical opossed to formal...I dont do things like that...but when showing how to do something instead of just saying \lim_{x\to\infty}\frac{1}{2^{x}}=0 I like to show WHY it is
    ...it is just my preference...but you are correct in that it is informal and not to be done on tests
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  5. #5
    Moo
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    Quote Originally Posted by Mathstud28 View Post
    ...it is just my preference...but you are correct in that it is informal and not to be done on tests
    Just my opinion :
    I think it's not very wise to act this way.. People could say in a test "but someone wrote this ! so I can !"
    And that is the problem, it's your preference, but we're talking about an other one's exercise..
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